# Geometry Ch. 2 - Proofs

## 27 terms

### Definition of segment congruence

AB=CD if segment AB≅ segment CD

m∠A=m∠B if ∠A≅∠B

### Definition of a right angle

If an angle measures 90°, then it is a right angle.
If an angle is a right angle, then it measures 90°.

### Definition of perpendicular

BA ⊥ BC
∠ABC is a right angle

### Definition of a linear pair

A linear pair is two adjacent angles whose exterior sides form a straight line

### Definition of midpoint

M is the midpoint of AB
AM is congruent to MB

### Definition of an angle bisector

Ray BX bisects <ABC
<ABX is congruent to <XBC

### Right Angle Congruence Theorem

<A and <B are right angles
<A is congruent to <B

### Vertical Angles Congruence Theorem

all vertical angles are congruent

B is between A and A
AB + BC = AC

X is in the interior of <RST
m<RSX + m<XST = m<RST

### Linear Pair Postulate

<1 and <2 form a linear pair
<1 and <2 are supplementary

x = y
x + 3 = y + 3

a = b
a - c = b - c

### Definition of complementary angles

<R and <S are complementary
m<R + m<S = 90 degrees

### Definition of supplementary angles

<1 and <2 are supplementary
m<1 + m<2= 180 degrees

### Definition of bisector

line l bisects AB at M
M is the midpoint of AB

m<1 = m<2
2m<1 = 2m<2

2x = 8
x = 4

3(x + 7) = 15
3x + 21 = 15

Simplify

Given AB
AB = AB

### Symmetric Property of Congruence

AB is congruent to CD
CD is congruent to AB

a = b and b = c
a = c

### Substitution Property of Equality

AB + CD = EF + FG and XY = FG
AB + CD = EF + XY

### Congruent Supplements Theorem

<S and <R are supplementary
<T and <R are supplementary
<S is congruent to <T

### Congruent Complements Theorem

<S and <R are complementary
<T and <R are complementary
<S is congruent to <T